Determining Distance to Type Ia Supernovae Through Analysis of G-band Light Curve Data
Advisor: Mr. John Hanlon
Internship Location: KLA, CA
Onsite Mentor: Yun
The Universe harbors a few fundamental questions, with one of them being, "how far?" Type Ia Supernovae — stellar explosions known as standard candles due to their consistent luminosity — allows us to answer this question by acting as the tools for measuring galactic distances. Previous attempts by NASA to measure the distance to galaxy NGC 5643 all employed the Tully-Fisher method, which has a much greater uncertainty compared to analyzing the light curve of a Type Ia supernova within the galaxy. This project will take raw data from the SDSS telescopes and apply a variety of data-correction techniques (correcting for exposure times, galactic dust, and standard stars) to plot a graph of supernova magnitude vs. time. Taking the distance modulus — the difference between the peak magnitude and the magnitude 15 days later — we will be able to find the distance to the supernova and the galaxy it is contained in. Finding the distance to faraway galaxies is also essential for calculating the expansion rate of the universe, and other scientists could use the results of this project in their own research
Project Blog
Week 0: Introduction and Background
Hello, everyone! Welcome to the first blog post of my senior project. Over the course of my project, I will be finding the distances to cosmic objects. My future posts will go further into depth about the process and the overall science surrounding cosmology.
I’ve always been interested in space. I’ve been trying to read books such as The Black Hole War since long before I’ve been able to understand cross products vs. dot products. I’ve always wanted to better understand relativity and the black hole information paradox, to find out all the hows and whys surrounding… space. Space is often considered the ultimate mystery, and it's something I want to unravel.
So for my senior project, I decided to dabble in astrophysics and find the distance to type Ia supernovae from raw telescope data.
Why? Well, I hope to answer one of the fundamental questions about our universe: How far? By analyzing the light curves of type Ia supernovae, we seek to answer fundamental questions related to the expansion of the universe, the nature of dark energy, and the reliability of Type Ia Supernovae as standard candles. The project will contribute to refining the cosmic distance ladder, providing crucial insights into the large-scale structure of the universe by refining cosmological models and determining fundamental parameters like the Hubble constant. Earlier measurements of NGC 5643’s distance have already been calculated using the Tully Fisher method, but this method can yield inaccurate results. My research also aims to offset the 20% uncertainty of the Tully-Fisher method through more accurate measurements using standard candles.
Type Ia supernovae are often referred to as "standard candles" due to their consistent luminosity. By accurately determining the distance to a Type Ia supernova, researchers can use it as a standard reference point for measuring cosmic distances, which is crucial for understanding the scale and structure of the universe. Studying the distance to a Type Ia supernova in its host galaxy provides valuable information about the galaxy itself. This helps astronomers understand the distribution, evolution, and dynamics of galaxies in the universe. And since Type Ia supernovae result from the explosion of white dwarf stars in binary systems, analyzing their light curves provide further insight into the life cycle of stars and the conditions under which Type Ia supernovae occur.
Finding the distance to faraway galaxies is also essential for calculating the expansion rate of the universe, which requires a combination of finding the redshifts, recessional velocities, and distances to galaxies. And once we know the expansion rate, we can predict the future state of the universe.
I’m excited to start finding the answers to these questions I’ve had ever since my childhood. Stay tuned for updates!
Week 1: Type Ia Supernovae, the Cosmic Distance Ladder, and alternative methods of measuring distance
Welcome back to our journey! Last week, we delved into the captivating realm of Type Ia supernovae and their significance in unraveling the mysteries of the universe. This week, we will explore the role of these stellar explosions as standard candles, and the intricate web of the cosmic distance ladder.
Understanding Type Ia Supernovae:
Before we delve into their significance as cosmic yardsticks, let's revisit the enigmatic nature of Type Ia supernovae. These cosmic detonations, born from white dwarf stars in binary systems, have uniform luminosity profiles. Unlike other types of supernovae, Type Ia explosions exhibit consistent brightness, making them very useful tools for measuring cosmic distances.
Significance as Standard Candles:
Type Ia supernovae serve as beacons in space. Their uniform luminosity allows researchers to calibrate distance measurements with remarkable precision, similar to using standard rulers to gauge lengths. By comparing the observed brightness of Type Ia supernovae with their intrinsic luminosity, scientists can accurately determine their distance from Earth.
The Cosmic Distance Ladder:
But how do astronomers harness the luminous glow of Type Ia supernovae to measure cosmic distances? Enter the cosmic distance ladder, a hierarchical framework of distance measurement techniques that spans the vast reaches of the universe. At its foundation lie nearby objects whose distances can be measured directly, such as parallax measurements of nearby stars. Building upon these foundational rungs, astronomers ascend the ladder, using increasingly sophisticated methods to measure distances to ever more distant celestial objects.
Reviewing Other Methods of Determining Distance:
While Type Ia supernovae represent a powerful tool in the astronomer's arsenal, they are not the sole method for measuring cosmic distances. Alternative techniques, such as the cosmic redshift and the Tully-Fisher relation, offer complementary approaches for gauging the vastness of space. However, each method has its limitations, from the inherent uncertainties in measuring galaxy redshifts to the challenges of calibrating the luminosity of distant galaxies.
Another popular method to measure distances is by using Cepheid variables — stars which pulsate rapidly, varying in size and temperature, and with well-defined period and amplitude. There is a strong direct relationship between a Cepheid variable’s luminosity and pulsation period, which means that by observing its pulsation period, one can find the true luminosity of a Cepheid. And once true luminosity is known, distance becomes trivial to calculate.
Over the next few days, I will be finishing up an exercise where I take the light curves for different Cepheids and calculate the average apparent magnitudes and the periods (in days). So far, I have found the mean absolute magnitude through extrapolating on the period-luminosity plot. Using this information, I substituted into the distance-modulus formula, which gives the distance to the Cepheid. My future work this week consists of replicating my work for different data inputs.
Some of the chief problems when using Cepheid variables are the effects of metallicity, photometric contamination (star-blending), and galactic extinction on distance measurements. For instance, the amount of gas and dust in the sky when the picture was taken can influence measurements.
I looked at several research papers using Cepheid variables to estimate the Hubble constant, and calculated values have ranged between 60 km/s/Mpc to 80 km/s/Mpc. This suggests that my future roadblocks will consist chiefly of massaging out the problems in my raw data.
Our Journey Ahead:
As we venture further into the cosmic wilderness, we will continue to explore the intricacies of Type Ia supernovae and the cosmic distance ladder. In the coming weeks, we will unravel the mysteries of these stellar explosions, charting a course through the cosmic expanse as we seek to unlock the secrets of the universe.
Until next time.
Week 2: Unveiling the Cosmos - Dark Energy, Universal Expansion, and the Legacy of Hubble
Hello, everyone! Welcome back to our cosmic journey! Last week, we covered some alternative methods of finding cosmological distances, such as using Cepheid variables or the Tully-Fisher relation. Let's quickly revisit each concept. Methods such as the Tully-Fisher relation, cosmic redshift, and Cepheid variables play significant roles in measuring cosmic distances, each with its own set of challenges like metallicity effects, photometric contamination, and galactic extinction. Cepheid variables, which vary in brightness with well-defined periods, offer a direct way to measure distances by using the relationship between their pulsation period and luminosity.
This week, we embark on an enlightening exploration of the importance of distance measurements. Our study will center around two topics: dark energy and the Hubble Constant. We'll also reflect on the significance of Type Ia supernovae in measuring cosmic distances and how this relates to Hubble's groundbreaking discovery.
The Mysterious Fabric of Dark Energy:
Dark energy is intrinsically related to the accelerating expansion of the universe. This mysterious energy, which permeates all of space, acts as a counterbalance to gravity, propelling the cosmos to expand at an ever-increasing rate. By reviewing the effects of dark energy and its intricate relationship with Hubble's Law, we gain insight into one of the most puzzling phenomena in modern cosmology. While no one knows exactly what dark energy and dark matter are, some theories exist which postulate dark matter to be a superfluid.
Calculating the Expansion of the Universe:
What exactly is the Hubble constant? Put simply, it is a parameter which represents the rate of expansion of the universe. It describes the relationship between the distances of galaxies and their recessional velocities (the speed they are moving away from us).
I started a hands-on exercise to learn more about how Hubble actually found his constant. Analyzing distance measurements and recessional velocities to several galaxies (of which these values are known) results in all the information we need to calculate Hubble’s constant. I created a graph of the values, with distance (in megaparsecs) on the x-axis and velocity (in kilometers per second) on the y-axis. The slope of the line of best fit is the estimated value of the Hubble constant, in units of km/s/Mpc. Funnily enough, Hubble used Cepheid variables to find his distance measurements, while I’ll be using Type Ia supernovae.
Why is this important? Well, Hubble’s Law can be expressed as v=H0×d, where v is the recessional velocity of a galaxy, H0 is the Hubble constant, and d is the distance of the galaxy from an observer. So if we look at two galaxies who are some distance d, at some point in time, they were touching. This point in time is the moment of the Big Bang. Thus, the age of the universe is around the reciprocal of the Hubble constant, or around 13.4 billion years old. This is how some simple distance measurements using Cepheid variables lead to larger discoveries down the line.
Role of Redshifts:
When the light from faraway galaxies travels through expanding space, its wavelengths get stretched, which makes the light appear redder than it originally was. Astronomers convert the amount of observed redshift into a measure of the velocity at which a galaxy is moving away from us. This is yet another piece of evidence for the expansion of the universe.
To better understand how redshifts are implemented, I solved for the distance versus redshift relations, where I worked out the luminosity distance-redshift relation for a given scale factor a(t) of the universe.
Journeying Forward:
The concepts of dark energy, the expanding universe, and the legacy of Hubble provide us with a richer understanding of the cosmos. Join us next week as we venture into the nitty-gritty of type Ia supernovae and what makes them so useful to astronomers.
Until next time.
Week 3: Stellar Evolution, Defining Characteristics and Typical Luminosity changes of Type Ia Supernovae
Hello and welcome to another installment of our journey! Last week we covered how Hubble’s constant was found — through distance calculations — and how we use that constant to find out more about our universe, such as expansion rate and age.
This week, our adventure will take us from the birth of stars to their spectacular demise, where we learn about the history behind supernovae. Then, we explore some defining characteristics of Type Ia supernovae and how these characteristics lead towards our eventual distance calculation. And finally, I'll explain my first steps to obtaining a distance out of raw images.
Stellar Evolution and Supernovae:
Typically, main-sequence stars fuse hydrogen until only helium is available, which causes the nuclear fusion reaction within the star to lessen, thereby decreasing pressure. The star swells, turning into a red giant, until gravity squishes the star into a state where helium can be fused. The star continues this process with heavier and heavier elements (carbon, oxygen), and then begins to shed its outer layers as its inner temperature increases. When temperatures exceed 30,000 K, the emitted ultraviolet photons number greatly enough to ionize the ejected atmosphere, creating a planetary nebula. This leaves the degenerated star as a white dwarf, surrounded by a glowing gas cloud.
Type Ia supernovae occur in binary star systems, where one star — a white dwarf — orbits a larger star, slowly accreting mass from its companion, which can be anything from a much larger star to an even smaller white dwarf. This mass accretion eventually reaches a limit, known as the Chandrasekhar limit (around 1.44 solar masses), where the outwards electron degeneracy pressure becomes lesser than the force of gravity. The star collapses, which releases energy as a supernova. This process is marked by a specific signature in the electromagnetic spectrum and a uniformity in luminosity, making type Ia supernovae invaluable as "standard candles" for measuring cosmic distances, as they all grow unstable near the same mass point (and thus, release similar amounts of energy).
A Closer Look at the Explosion Mechanism:
However, the explosion which occurs when the white dwarf reaches 1.44 solar masses is more complex than simply gravity > electron degeneracy pressure. As the white dwarf approaches the Chandrasekhar limit, the pressure and temperature at its core rise dramatically, setting the stage for a runaway nuclear fusion reaction.
The heart of a white dwarf is composed primarily of carbon and oxygen. When the core temperature reaches 600 million K, carbon fusion ignites in a fraction of a second, followed by oxygen fusion. This sudden onset of fusion unleashes an immense amount of energy.
Initially, the fusion front moves outward in a subsonic combustion wave known as deflagration. However, high temperatures and turbulence can trigger a faster, supersonic wave known as detonation. This transition is crucial, as it accelerates the energy release. Rayleigh-Taylor instability, where lighter, hot material pushes through the denser star material, plays a pivotal role in mixing up the star (as expanding gas in the core accelerates into denser outer-shell gas) and increasing the energy of the supernova.
The Big Picture:
What matters here is that since the mass of the star is directly proportional to energy release, and when one remembers that energy release is proportional to absolute luminosity (brightness), all white dwarf supernovae have the same absolute luminosities, from which distance can be calculated (after one measures the apparent luminosity and performs some calculations).
Looking Ahead:
Now that we have most of the background information ready, next week will be full of data and raw images from telescopes in New Mexico. Thanks for reading my blog, and stay tuned for next week’s issue!
Week 4: Exploring Data, Harnessing Source Extractor, Tedious Sorting
Hello, everyone! Welcome back to my blog. Last week, we explored the intricate mechanisms behind white dwarf supernovae, and examined the fusion processes that create the supernovae’s uniform luminosities.
This week will deal with actual data, taken by the Sloan Digital Sky Survey (SDSS) telescopes in New Mexico. I will first extract the brightness values of all the stars in each data file, and then I’ll find which brightness value corresponds to my supernova (as that’s the one I want to analyze).
Dealing with Data:
My data consists of 90 FITS files. FITS stands for Flexible Image Transport System and is a common data format in astronomy. Each file contains the time and date of the picture as well as the exposure time of the camera. I used SAOImage ds9 to view each file. The pictures are of galaxy NGC 5643 and the surrounding sky. My first goal is to actually find my supernova — there are probably trillions of stars in just a small section of the image. Here’s an example of what one of the pictures looks like:
You can clearly see the galaxy there. NGC 5643 is a spiral galaxy — its spiral arms are very distinct. Now, the goal is to find the supernova. Chances are, it will be in or near the galaxy, as that has the largest density of stars anywhere in the picture. My strategy for this was to find the dot with large changes in brightnesses (since supernovae outshine galaxies at first, but quickly fade away).
After going through multiple files, I finally found my supernova!
The supernova is the brightest dot in the image, and the bright swirls at the top left are parts of NGC 5643.
Harnessing Source Extractor:
Now it's time to code! Source Extractor is a program which extracts sources (or information about sources) from astronomical images. Sources refer to objects that produce or emit light — this can mean stars, galaxies, nebulae, or other astronomical phenomena. I’m using Source Extractor to extract the apparent magnitudes, or brightnesses, of every star in every image. And since I have close to 90 files to be scanned, I end up with a jumble of numbers — the brightnesses of every star in every file. However, you can set limits for Source Extractor to work on. I went through a few pictures, categorized the minimum and maximum brightnesses of the supernova, and set those as the limits for Source Extractor to work with. This cuts out a lot of stars for me to sort through.
I went and looked for the array with large magnitude changes, as this would probably be my supernova, and manually checked it against the brightness of the supernova in SAOImage ds9.
The Next Installment:
So, now I have an array of numbers representing the raw magnitudes of my supernova. The next few weeks will be devoted to correcting these numbers. Thank you for tuning in to this week's journey, and see you all next week!
Week 5: Debugging, More Source Extractor Shenanigans, and Exposure Times
Hello, everyone! Welcome back to my blog. In last week’s blog post, I detailed my first experiences with Source Extractor, a program used by astronomers to extract information from FITS files. I used Source Extractor to obtain the brightnesses (or magnitudes) of my supernova from the 81 FITS files I have access to and sorted each magnitude by date. Then, I went through my files to visually find my supernova, which I matched with the array of magnitudes I got from Source Extractor.
This week, I’ll be going over the first steps in my data processing journey.
A Small Problem:
Now this week was supposed to be about using the camera exposure times to correct my magnitudes (since longer exposure times artificially increase the brightnesses of the stars in these pictures), but I realized I had actually made a mistake last week.
Using Source Extractor is a little more complex than just telling it to extract the magnitudes. You have to specify a few parameters first, such as the zero point and aperture radii. To find the zero point, you have to observe a standard star (star with constant brightness). Then, find the catalog brightness of this star by referencing images from an online database, and simply subtract the two values. The difference is the zero point, which I used to calibrate all the magnitudes of my supernova.
Another parameter needed by Source Extractor is aperture radius, which calculates magnitudes within circular radii. What this means is that if you specify the minimum aperture radius to be extremely large, you will not log a lot of stars — which is useful if the object you are trying to examine is very large, as you can pinpoint your data to your target much more easily. However, it turns out that previously I had made a mistake when getting my magnitudes — I used an aperture size that was slightly too small, and Source Extractor did not log the magnitude of my supernova for two of my files.
I had to spend a day and a half fixing this, since this required me to start over.
The Rest of the Week:
Since I wasted so much time on this mistake, I didn’t actually get to the part where I use exposure times to correct my magnitudes. I spent another day extracting all my exposure times. The reason it took so long was that the file generated with the extracted exposure times kept showing up in the wrong place for a while, which was frustrating.
Anyways, this week was mostly full of debugging and problem-solving, which is why my progress is less than I would have liked. I suppose that I still did end up achieving half of my stated goal, which was to obtain an array with all the exposure times nicely laid out.
With any luck, my next post will detail the actual corrections I used. Thank you for reading my blog, and see you all next time!
Week 6: Astropy, Exposure Times, Standard Stars, and Graphs
Hello, everyone! Welcome back to my blog. In last week’s post, I detailed a series of challenges encountered while trying to correct star magnitudes using camera exposure times. I also made a mistake by incorrectly setting the aperture size for the software, which led to Source Extractor not recognizing some instances of my supernova. This necessitated a redo of the work.
I started this week off with an array of the exposure times for each file, sorted by date. I’ll use this data to finally correct my magnitudes.
Correcting the Magnitudes:
So far, if I chart my supernova’s raw magnitude over time, I get this graph:
The ideal graph is a neat, orderly line that slowly rises, hits a peak, then quickly drops down (i.e. an exponential decay curve). This is partially reflected by my curve — you can see how the peak values are relatively smooth, but quickly devolve into chaos as the magnitudes decrease.
After I correct using exposure times, I should get a smoother curve. This is what my graph looks like after the correction:
It looks a lot messier, but it has actually been corrected. The curve is more pronounced — here is a version with better illustration:
You can see how now we can draw a line of best fit. All those values which seem really random will hopefully be corrected using standard stars, which is where I’ll extract the brightnesses of a nearby star from every image to use as a “standard”. This corrects for any inconsistencies between photographs (such as cloud cover, moisture, dust, etc.)
I started by first identifying a standard star — I chose USNOA2 0450-17805518, which is right next to my supernova. I identified the star using Sky Map (I entered my galaxy into their system and found an identifiable star). Sky Map tells me that the apparent magnitude of that constant star is 14.35.
However, I ran into another issue with extracting the magnitudes of this star in my images (some of my images are lined up improperly). I hope to resolve this over the weekend, and finish my corrections with my standard stars.
Thank you for reading my blog, and see you all next time!
Week 7: Applying Corrections Using Standard Stars, Equations, and Fixing Big Errors
Hello, everyone! Welcome back to my blog! In last week’s post, I detailed how I finished using exposure times to correct my data. I also began using standard stars to fix my data, and explained why having these constant stars as a reference matters.
This week, I’ll be (hopefully) finishing up my project’s standard star stint.
Standard Stars:
I had already chosen USNOA2 0450-17805518 (which is pretty much just a random boring star) for my standard star. I finally managed to successfully extract the counts (a value which can be converted into brightness) and stored my counts in an array. I used this equation to correct my values:
However, the graph I generated after was not very nice-looking. There were still some strange values which didn’t lie on the curve. This suggested that there was some problem with what I did. For reference, the graph at this point looked like this:
It looks a lot nicer, but a correct version would not have any outliers (or at max, one or two), since supernovae grow dimmer at a steady rate. I spent a few days going over my process and seeing if I could identify any errors.
I decided to see if my data would magically fix itself if I used another standard star. So I repeated the process for another star, and the problem persisted.
Whoops:
So it turns out that the actual magnitudes of the standard stars — which I got from Sky Map — were wrong. All my data is in the g-band, which is a specific wavelength of light. Stars can have different magnitudes at different wavelengths, and I forgot to check which band Sky Map defaults to (hint: it's not the g-band).
Sadly, I only recognized that mistake on the day that I’m posting this blog, which means that hopefully, by next week, we will have a nice-looking graph to look at.
Thank you for reading my blog, and see you all next time!
Week 8: Actually Applying Corrections Using Standard Stars, Extinction, Final Graphs
Hello, everyone! Welcome back to my blog! In last week’s post, I detailed my experiences working with standard stars. I had already extracted the magnitudes of my two standard stars, but I found the wrong apparent magnitude value (the value I got from Sky Map was for another light band).
Standard Stars (again):
I spent most of my Monday perusing different online databases. One of the biggest is the NASA/IPAC Extragalactic Database (NED), which I used to find some preliminary information about my galaxy. Sadly, that avenue quickly closed up when I couldn’t find them at all after a few hours of searching.
Eventually, I found information about my standard stars using the SIMBAD Astronomical Database, which listed out the different apparent magnitudes for each band of light.
So, I finally managed to apply my standard star corrections! This drastically lowered the amount of outliers.
The next step I did was to use extinction (the dust/gas which scatters light) to further correct my data. I found the extinction coefficient on NED, and subtracted it from all my magnitudes to get this graph:
As you can see, it looks a lot neater, which indicates that my process was done correctly (my previous blogs showcase messier, uncorrected-for graphs). Now, it’s time to jump into the calculations behind obtaining a distance value.
Thank you for reading my blog, and I'll see you all next time!
Week 9: Paper and Presentation
Hello, everyone! Welcome back to my blog! Last week, I finished generating the graph that represents my data after all my corrections. This week, I’ll use this finished graph to obtain a distance value.
An Important Scientific Paper:
I began my week with an in-depth reading of “The Carnegie Supernova Project: Analysis of the First Sample of Low-Redshift Type-Ia Supernovae” by Folatelli, et al. This paper describes a comprehensive study of many Type Ia supernovae. Folatelli and his colleagues analyzed the magnitude of these supernovae over time and calibrated their intrinsic colors to account for any reddening effects (where galactic dust absorbs/scatters blue light more than red light). Then, they investigated the absolute magnitudes of these supernovae across different light bands and their relationships with supernovae color and decline rate. Here is the link, if anyone is interested in further reading:
They found that there is a standard relationship between the supernovae’s decline rate and distance. They also found relationships between brightness and intrinsic color variation (which I don’t have the data for). The paper also put the precision of type Ia supernovae distances at 3%-4% (which is a lot higher than other methods).
Creating my Presentation:
The rest of my week was spent working on my slideshow. I did my best to cut out the boring parts, so hopefully everyone will understand my process on the big day. I did a practice run of my presentation with my internal advisor on Friday, and I’ll continue practicing over the next few weeks.
Next week’s blog will hopefully end with a distance number! Thank you for reading my blog, and see you all next time!
Week 10: The Final Distance
Hello, everyone! Welcome back to my blog! This will be the last blog post, so thank you for keeping up with my journey! Last week, I practiced my presentation and read up on how other scientists found the distance to other supernovae. This week, I’ll use the light curve of my supernova alongside the method described in a paper by Folatelli et al. to find the distance to my supernova.
The Method:
The general idea is that since all type Ia supernovae “go supernova” with the same amount of mass, the absolute magnitude of all type Ia supernovae will be constant. This means that we can find the distance if we know the apparent magnitude of the supernova (or how bright it looks from Earth), and simply use an equation relating brightness to distance to obtain our final answer. Why this phenomenon works is easy to understand — if you take a lightbulb and walk away from it, you find that it gets dimmer. By knowing how bright it is to your eyes and how bright it actually is (say, to a person right next to the bulb), you can calculate the distance.
The absolute magnitude of the supernova is denoted as MB. I took this value from several databases, where it was calculated through alternative (but more imprecise) methods of finding distances (such as the Tully-Fisher approximation). I took MB to be -19.17 for the g-band.
We also need to know the distance modulus, which is defined as m-M, or the difference between the apparent and absolute magnitudes. My value of apparent magnitude was taken from my graph.
Here are the actual equations I ended up using:
µ = m - M = 5*log(d/10 parsecs)
µsn= mB - MB - bx [△m15(B) - 1.1]
△m15(B) = mB(15) - mB(max)
What we want is µsn , or the distance modulus of our specific supernova. I took mB (the peak apparent magnitude of my supernova) from my graph — it is around 11.35. Next, bx (1.32) is the slope of the luminosity decline rate, which was calibrated using multiple supernovae (I took the value from Folatelli et. al). The term mB(15) represents the apparent magnitude 15 days later, which I also took from my graph. My data was sporadic, and there was no picture of my supernova taken precisely 15 days after the day it was brightest, so I approximated the magnitude 15 days after the peak. I approximated it to be around 12.07.
My µsn was calculated to be 31.02. Solving for d — 31.02 = 5 * log(d/10pc), so d is around 15995580 parsecs, which can be rounded to 16 megaparsecs (MPC). The latest estimates from NASA’s extragalactic database for the distance to the supernova range from 14-17 MPC — these estimates were calculated through less precise methods (such as the Tully-Fisher approximation, which has around a 20% error bound).
So after a lot of data manipulation and a few errors, we’ve finally arrived at a distance value! What made this process exciting for me was how similar it was to real research conducted at universities and labs around the world. Thanks for following my journey!
I’ll be presenting my project on May 18th at the Senior Project Symposium (Fremont Marriott Silicon Valley), so if you can make it to the event, be sure to check out my project!